Discrete Mathematics(MC123) 

Course description:  Set theory, relations and functions, posets, Hasse diagram and lattices. Fundamentals of logic (the laws of logic, rules of inferences, quantifiers, proofs of theorems).  Graphs (clique, independent set, vertex cover, degree, regular, complement,  tree, counting trees (Prufer Code), minimal spanning trees, Kruskal algorithm, Prim's algorithm , Euler's  formula, Kuratowski's theorem, five-color theorem  ). Fundamental principles of counting (permutations, combinations, Binomial theorem, multimonial coefficients, recurrence relation, solving linear recurrence relation  and generating function). Basic number theory (Modular arithmetic, primes and representation of integers, linear congruences,  etc.),  Boolean Algebra (Boolean functions, logic gates, minimization expressions, K-maps ).

Course Goals: The primary objective of the course is that students should learn a particular set of mathematical facts and how to apply them. In particular it teaches students how to think logically and mathematically through five important themes: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and applications and modeling. A successful discrete mathematics course should carefully blend and balance all five themes. 

Suggested Textbook/references:  

Elements of Discrete Mathematics, C.L. Liu., Tata McGraw-Hill Publishing Company Ltds. 2nd edition .

Discrete Mathematics and its Applications (7th Edition), Kenneth.H. Rosen, McGraw Hill International edition. 

Mott J. L. , Kandel A. and Baker T. P., Discrete Mathematics for Computer Scientists and Mathematicians, Second Edition, Prentice Hall India, 1986. 

 Thomas H. C., Leiserson C. E.; Rivest R. L.; Stein C., Introduction to Algorithms (2nd ed.). MIT Press and McGraw-Hill. 2001. 

Grading:  Test 1 (30%  ),  Test  2 (30%  ), Test 3 (40%  )